The Old Testament was pre-Christ. You could only go to heaven if you were without sin, which was impossible because Adam and Eve introduced sin into the world, OR if you made sacrifices to God such as an animal. The animal, such as a lamb, stood in for you and died in your place to cover your sins (the "blood of the lamb"). The new Testament is after God sent Christ. The "deal" changed then; Christ was without sin but died for ours. So he made it so that people don't have to be perfect to be able to go to heaven. Christ was the sacrifice, hence the "lamb of God".